Hedging Options with Different Time Units in the Pricing Models

This study examined the effects of the Greeks of the options and the trading results of delta hedging strategies, with three different time units or option-pricing models. These time units were calendar time, trading time and continuous time using discrete approximation (CTDA) time. The CTDA time model is a pricing model, that among others accounts for intraday and weekend, patterns in volatility. For the CTDA time model some additional theta measures, which were believed to be usable in trading, were developed. The study appears to verify that there were differences in the Greeks with different time units. It also revealed that these differences influence the delta hedging of options or portfolios. Although it is difficult to say anything about which is the most usable of the different time models, as this much depends on the traders view of the passing of time, different market conditions and different portfolios, the CTDA time model can be viewed as an attractive alternative.

The Pricing of American Put Options on Stock with Dividends

Pricing American put options on dividend-paying stocks has largely been ignored in the option pricing literature because the problem is mathematically complex and valuation usually resorts to computationally expensive and impractical pricing applications. This paper computed a simulation study, using two different approximation methods for the valuation of American put options on a stock with known discrete dividend payments. This to find out if there were pricing errors and to find out which could be the most usable method for practical users. The option pricing models used in the study was the dividend approximation by Blomeyer (1986) and the one by Barone-Adesi and Whaley (1988). The study showed that the approximation method by Blomeyer worked satisfactory for most situations, but some errors occur for longer times to the dividend payment, for smaller dividends and for in-the-money options. The approximation method by Barone-Adesi and Whaley worked well for in-the-money options and at-the-money options, but had serious pricing errors for out-of-the-money options. The conclusion of the study is that a combination of the both methods might be preferable to any single model.

Going Multinational under Exchange Rate Uncertainty

Published as an article in: Journal of International Money and Finance, 2010, vol. 29, issue 6, pages 1171-1191.

Latent Variable Models for Stochastic Discount Factors.

Latent variable models in finance originate both from asset pricing theory and time series analysis. These two strands of literature appeal to two different concepts of latent structures, which are both useful to reduce the dimension of a statistical model specified for a multivariate time series of asset prices. In the CAPM or APT beta pricing models, the dimension reduction is cross-sectional in nature, while in time-series state-space models, dimension is reduced longitudinally by assuming conditional independence between consecutive returns, given a small number of state variables. In this paper, we use the concept of Stochastic Discount Factor (SDF) or pricing kernel as a unifying principle to integrate these two concepts of latent variables. Beta pricing relations amount to characterize the factors as a basis of a vectorial space for the SDF. The coefficients of the SDF with respect to the factors are specified as deterministic functions of some state variables which summarize their dynamics. In beta pricing models, it is often said that only the factorial risk is compensated since the remaining idiosyncratic risk is diversifiable. Implicitly, this argument can be interpreted as a conditional cross-sectional factor structure, that is, a conditional independence between contemporaneous returns of a large number of assets, given a small number of factors, like in standard Factor Analysis. We provide this unifying analysis in the context of conditional equilibrium beta pricing as well as asset pricing with stochastic volatility, stochastic interest rates and other state variables. We address the general issue of econometric specifications of dynamic asset pricing models, which cover the modern literature on conditionally heteroskedastic factor models as well as equilibrium-based asset pricing models with an intertemporal specification of preferences and market fundamentals. We interpret various instantaneous causality relationships between state variables and market fundamentals as leverage effects and discuss their central role relative to the validity of standard CAPM-like stock pricing and preference-free option pricing.

Pricing the options inherent in leased commercial property: a UK case study

This paper sets out the findings of a group of research and development projects carried out at the Department of Real Estate & Planning at the University of Reading and at Oxford Property Systems over the period 1999 – 2003. The projects have several aims: these are to identify the fundamental drivers of the pricing of different lease terms in the UK property sector; to identify current and best market practice and uncover the main variations in lease terms; to identify key issues in pricing lease terms; and to develop a model for the pricing of rent under a variety of lease variations. From the landlord’s perspective, the main factors driving the required ‘compensation’ for a lease term amendment include expected rental volatility, expected probability of tenant vacation, and the expected costs of tenant vacation. These data are used in conjunction with simulation technology to reflect the options inherent in certain lease types to explore the required rent adjustment. The resulting cash flows have interesting qualities which illustrate the potential importance of option pricing in a non-complex and practical way.

Pricing short leases and break clauses using simulation methodology

This paper examines the changes in the length of commercial property leases over the last decade and presents an analysis of the consequent investment and occupational pricing implications for commercial property investmentsIt is argued that the pricing implications of a short lease to an investor are contingent upon the expected costs of the letting termination to the investor, the probability that the letting will be terminated and the volatility of rental values.The paper examines the key factors influencing these variables and presents a framework for incorporating their effects into pricing models.Approaches to their valuation derived from option pricing are critically assessed. It is argued that such models also tend to neglect the price effects of specific risk factors such as tenant circumstances and the terms of break clause. Specific risk factors have a significant bearing on the probability of letting termination and on the level of the resultant financial losses. The merits of a simulation methododology are examined for rental and capital valuations of short leases and properties with break clauses.It is concluded that in addition to the rigour of its internal logic, the success of any methodology is predicated upon the accuracy of the inputs.The lack of reliable data on patterns in, and incidence of, lease termination and the lack of reliable time series of historic property performance limit the efficacy of financial models.

Essays in macroeconomy and dynamic term-structure models

This thesis is composed of three articles with the subjects of macroeconomics and - nance. Each article corresponds to a chapter and is done in paper format. In the rst article, which was done with Axel Simonsen, we model and estimate a small open economy for the Canadian economy in a two country General Equilibrium (DSGE) framework. We show that it is important to account for the correlation between Domestic and Foreign shocks and for the Incomplete Pass-Through. In the second chapter-paper, which was done with Hedibert Freitas Lopes, we estimate a Regime-switching Macro-Finance model for the term-structure of interest rates to study the US post-World War II (WWII) joint behavior of macro-variables and the yield-curve. We show that our model tracks well the US NBER cycles, the addition of changes of regime are important to explain the Expectation Theory of the term structure, and macro-variables have increasing importance in recessions to explain the variability of the yield curve. We also present a novel sequential Monte-Carlo algorithm to learn about the parameters and the latent states of the Economy. In the third chapter, I present a Gaussian A ne Term Structure Model (ATSM) with latent jumps in order to address two questions: (1) what are the implications of incorporating jumps in an ATSM for Asian option pricing, in the particular case of the Brazilian DI Index (IDI) option, and (2) how jumps and options a ect the bond risk-premia dynamics. I show that jump risk-premia is negative in a scenario of decreasing interest rates (my sample period) and is important to explain the level of yields, and that gaussian models without jumps and with constant intensity jumps are good to price Asian options.

Orthogonal gamma-based expansions for volatility option prices under jump-diffusion dynamics

In my work I derive closed-form pricing formulas for volatility based options by suitably approximating the volatility process risk-neutral density function. I exploit and adapt the idea, which stands behind popular techniques already employed in the context of equity options such as Edgeworth and Gram-Charlier expansions, of approximating the underlying process as a sum of some particular polynomials weighted by a kernel, which is typically a Gaussian distribution. I propose instead a Gamma kernel to adapt the methodology to the context of volatility options. VIX vanilla options closed-form pricing formulas are derived and their accuracy is tested for the Heston model (1993) as well as for the jump-diffusion SVJJ model proposed by Duffie et al. (2000).

Hybrid wind-diesel power plant valuation and optimization using real option theory and dynamic programming

El sistema de energía eólica-diesel híbrido tiene un gran potencial en la prestación de suministro de energía a comunidades remotas. En comparación con los sistemas tradicionales de diesel, las plantas de energía híbridas ofrecen grandes ventajas tales como el suministro de capacidad de energía extra para "microgrids", reducción de los contaminantes y emisiones de gases de efecto invernadero, y la cobertura del riesgo de aumento inesperado del precio del combustible. El principal objetivo de la presente tesis es proporcionar nuevos conocimientos para la evaluación y optimización de los sistemas de energía híbrido eólico-diesel considerando las incertidumbres. Dado que la energía eólica es una variable estocástica, ésta no puede ser controlada ni predecirse con exactitud. La naturaleza incierta del viento como fuente de energía produce serios problemas tanto para la operación como para la evaluación del valor del sistema de energía eólica-diesel híbrido. Por un lado, la regulación de la potencia inyectada desde las turbinas de viento es una difícil tarea cuando opera el sistema híbrido. Por otro lado, el bene.cio económico de un sistema eólico-diesel híbrido se logra directamente a través de la energía entregada a la red de alimentación de la energía eólica. Consecuentemente, la incertidumbre de los recursos eólicos incrementa la dificultad de estimar los beneficios globales en la etapa de planificación. La principal preocupación del modelo tradicional determinista es no tener en cuenta la incertidumbre futura a la hora de tomar la decisión de operación. Con lo cual, no se prevé las acciones operativas flexibles en respuesta a los escenarios futuros. El análisis del rendimiento y simulación por ordenador en el Proyecto Eólico San Cristóbal demuestra que la incertidumbre sobre la energía eólica, las estrategias de control, almacenamiento de energía, y la curva de potencia de aerogeneradores tienen un impacto significativo sobre el rendimiento del sistema. En la presente tesis, se analiza la relación entre la teoría de valoración de opciones y el proceso de toma de decisiones. La opción real se desarrolla con un modelo y se presenta a través de ejemplos prácticos para evaluar el valor de los sistemas de energía eólica-diesel híbridos. Los resultados muestran que las opciones operacionales pueden aportar un valor adicional para el sistema de energía híbrida, cuando esta flexibilidad operativa se utiliza correctamente. Este marco se puede aplicar en la optimización de la operación a corto plazo teniendo en cuenta la naturaleza dependiente de la trayectoria de la política óptima de despacho, dadas las plausibles futuras realizaciones de la producción de energía eólica. En comparación con los métodos de valoración y optimización existentes, el resultado del caso de estudio numérico muestra que la política de operación resultante del modelo de optimización propuesto presenta una notable actuación en la reducción del con- sumo total de combustible del sistema eólico-diesel. Con el .n de tomar decisiones óptimas, los operadores de plantas de energía y los gestores de éstas no deben centrarse sólo en el resultado directo de cada acción operativa, tampoco deberían tomar decisiones deterministas. La forma correcta es gestionar dinámicamente el sistema de energía teniendo en cuenta el valor futuro condicionado en cada opción frente a la incertidumbre. ABSTRACT Hybrid wind-diesel power systems have a great potential in providing energy supply to remote communities. Compared with the traditional diesel systems, hybrid power plants are providing many advantages such as providing extra energy capacity to the micro-grid, reducing pollution and greenhouse-gas emissions, and hedging the risk of unexpected fuel price increases. This dissertation aims at providing novel insights for assessing and optimizing hybrid wind-diesel power systems considering the related uncertainties. Since wind power can neither be controlled nor accurately predicted, the energy harvested from a wind turbine may be considered a stochastic variable. This uncertain nature of wind energy source results in serious problems for both the operation and value assessment of the hybrid wind-diesel power system. On the one hand, regulating the uncertain power injected from wind turbines is a difficult task when operating the hybrid system. On the other hand, the economic profit of a hybrid wind-diesel system is achieved directly through the energy delivered to the power grid from the wind energy. Therefore, the uncertainty of wind resources has increased the difficulty in estimating the total benefits in the planning stage. The main concern of the traditional deterministic model is that it does not consider the future uncertainty when making the dispatch decision. Thus, it does not provide flexible operational actions in response to the uncertain future scenarios. Performance analysis and computer simulation on the San Cristobal Wind Project demonstrate that the wind power uncertainty, control strategies, energy storage, and the wind turbine power curve have a significant impact on the performance of the system. In this dissertation, the relationship between option pricing theory and decision making process is discussed. A real option model is developed and presented through practical examples for assessing the value of hybrid wind-diesel power systems. Results show that operational options can provide additional value to the hybrid power system when this operational flexibility is correctly utilized. This framework can be applied in optimizing short term dispatch decisions considering the path-dependent nature of the optimal dispatch policy, given the plausible future realizations of the wind power production. Comparing with the existing valuation and optimization methods, result from numerical example shows that the dispatch policy resulting from the proposed optimization model exhibits a remarkable performance in minimizing the total fuel consumption of the wind-diesel system. In order to make optimal decisions, power plant operators and managers should not just focus on the direct outcome of each operational action; neither should they make deterministic decisions. The correct way is to dynamically manage the power system by taking into consideration the conditional future value in each option in response to the uncertainty.

The meaning of implied volatility in pricing stock options traded in options markets

Ph.D. in the Faculty of Business Administration

A comparison of alternative bankruptcy prediction models

Early models of bankruptcy prediction employed financial ratios drawn from pre-bankruptcy financial statements and performed well both in-sample and out-of-sample. Since then there has been an ongoing effort in the literature to develop models with even greater predictive performance. A significant innovation in the literature was the introduction into bankruptcy prediction models of capital market data such as excess stock returns and stock return volatility, along with the application of the Black–Scholes–Merton option-pricing model. In this note, we test five key bankruptcy models from the literature using an upto- date data set and find that they each contain unique information regarding the probability of bankruptcy but that their performance varies over time. We build a new model comprising key variables from each of the five models and add a new variable that proxies for the degree of diversification within the firm. The degree of diversification is shown to be negatively associated with the risk of bankruptcy. This more general model outperforms the existing models in a variety of in-sample and out-of-sample tests.

Buy low, sell high

We consider online trading in a single security with the objective of getting rich when its price ever exhibits a large upcrossing, without risking bankruptcy. We investigate payoff guarantees that are expressed in terms of the extremity of the upcrossings. We obtain an exact and elegant characterisation of the guarantees that can be achieved. Moreover, we derive a simple canonical strategy for each attainable guarantee.

Mathematical Aspects of Financial Markets with Frictions

Frictions are factors that hinder trading of securities in financial markets. Typical frictions include limited market depth, transaction costs, lack of infinite divisibility of securities, and taxes. Conventional models used in mathematical finance often gloss over these issues, which affect almost all financial markets, by arguing that the impact of frictions is negligible and, consequently, the frictionless models are valid approximations. This dissertation consists of three research papers, which are related to the study of the validity of such approximations in two distinct modeling problems. Models of price dynamics that are based on diffusion processes, i.e., continuous strong Markov processes, are widely used in the frictionless scenario. The first paper establishes that diffusion models can indeed be understood as approximations of price dynamics in markets with frictions. This is achieved by introducing an agent-based model of a financial market where finitely many agents trade a financial security, the price of which evolves according to price impacts generated by trades. It is shown that, if the number of agents is large, then under certain assumptions the price process of security, which is a pure-jump process, can be approximated by a one-dimensional diffusion process. In a slightly extended model, in which agents may exhibit herd behavior, the approximating diffusion model turns out to be a stochastic volatility model. Finally, it is shown that when agents' tendency to herd is strong, logarithmic returns in the approximating stochastic volatility model are heavy-tailed. The remaining papers are related to no-arbitrage criteria and superhedging in continuous-time option pricing models under small-transaction-cost asymptotics. Guasoni, Rásonyi, and Schachermayer have recently shown that, in such a setting, any financial security admits no arbitrage opportunities and there exist no feasible superhedging strategies for European call and put options written on it, as long as its price process is continuous and has the so-called conditional full support (CFS) property. Motivated by this result, CFS is established for certain stochastic integrals and a subclass of Brownian semistationary processes in the two papers. As a consequence, a wide range of possibly non-Markovian local and stochastic volatility models have the CFS property.

Evaluating the Predictability of the Volatility Smile Using Return Distributions

In this paper, we examine the predictability of observed volatility smiles in three major European index options markets, utilising the historical return distributions of the respective underlying assets. The analysis involves an application of the Black (1976) pricing model adjusted in accordance with the Jarrow-Rudd methodology as proposed in 1982. Thereby we adjust the expected future returns for the third and fourth central moments as these represent deviations from normality in the distributions of observed returns. Thus, they are considered one possible explanation to the existence of the smile. The obtained results indicate that the inclusion of the higher moments in the pricing model to some extent reduces the volatility smile, compared with the unadjusted Black-76 model. However, as the smile is partly a function of supply, demand, and liquidity, and as such intricate to model, this modification does not appear sufficient to fully capture the characteristics of the smile.

Smiling under stochastic volatility

This paper studies the behavior of the implied volatility function (smile) when the true distribution of the underlying asset is consistent with the stochastic volatility model proposed by Heston (1993). The main result of the paper is to extend previous results applicable to the smile as a whole to alternative degrees of moneyness. The conditions under which the implied volatility function changes whenever there is a change in the parameters associated with Hestons stochastic volatility model for a given degree of moneyness are given.